The temperaments listed are 29edo-distinct, meaning that they are all different even if tuned in 29edo. The ordering is by increasing complexity of 3. The temperament of lowest TE complexity supported by the patent val was chosen as the representative for each class of edo-distinctness.

5-limit temperaments

Period generator	Wedgie	Name	Complexity	Commas
29 12	<<1 -8 -15]]	Helmholtz	3.103	32805/32768
29 6	<<2 13 16]]	Immunity	4.157	1638400/1594323
29 4	<<3 5 1]]	Porcupine	1.663	250/243
29 3	<<4 -3 -14]]	Negri	2.739	16875/16384
29 14	<<5 18 17]]		5.519	409600000/387420489
29 2	<<6 -19 -44]]		8.646	18160335421875/17592186044416
29 10	<<7 2 -13]]		3.303	78125/73728
29 13	<<8 23 18]]		7.012	102400000000/94143178827
29 11	<<9 -14 -43]]		8.269	9341736328125/8796093022208
29 7	<<10 7 -12]]		4.455	9765625/8957952
29 9	<<11 -1 -27]]		5.836	146484375/134217728
29 1	<<17 9 -25]]		7.664	762939453125/660451885056
29 8	<<13 12 -11]]		5.857	1220703125/1088391168
29 5	<<15 -4 -41]]		8.498	2471923828125/2199023255552

7-limit temperaments

Period generator	Wedgie	Name	Complexity	Commas
29 12	<<1 -8 -14 -15 -25 -10]]	Garibaldi	3.823	225/224 3125/3087
29 6	<<2 13 1 16 -4 -34]]	Immunity	3.651	49/48 2240/2187
29 4	<<3 5 16 1 17 23]]	Porky	3.362	225/224 250/243
29 3	<<4 -3 2 -14 -8 13]]	Negri	2.245	49/48 225/224
29 14	<<5 18 17 17 13 -11]]		4.821	686/675 2240/2187
29 2	<<6 10 3 2 -12 -21]]	Nautilus	2.943	49/48 250/243
29 10	<<7 2 18 -13 9 36]]		4.251	225/224 6125/5832
29 13	<<8 23 4 18 -16 -55]]		6.241	49/48 560000/531441
29 11	<<9 15 19 3 5 2]]	Ammonite	4.506	250/243 686/675
29 7	<<10 7 5 -12 -20 -8]]		3.751	49/48 3125/3024
29 9	<<11 -1 20 -27 1 49]]		5.909	225/224 84035/78732
29 1	<<17 9 23 -25 -11 28]]		6.682	686/675 21875/20736
29 8	<<13 12 21 -11 -3 15]]		5.238	686/675 3125/3024
29 5	<<14 4 7 -26 -28 5]]		5.436	49/48 78125/73728

11-limit temperaments

Period generator	Wedgie	Name	Complexity	Commas
29 12	<<1 -8 -14 -18 -15 -25 -32 -10 -14 -2]]	Cassandra	3.897	100/99 225/224 245/242
29 6	<<2 13 1 -7 16 -4 -18 -34 -61 -23]]	Immunity	3.977	49/48 55/54 896/891
29 4	<<3 5 16 4 1 17 -4 23 -8 -44]]	Porky	3.020	55/54 100/99 225/224
29 3	<<4 -3 2 15 -14 -8 10 13 45 35]]	Negroni	3.110	49/48 55/54 225/224
29 14	<<5 -11 -12 -3 -29 -33 -22 3 31 33]]	Tritonic	4.596	121/120 225/224 441/440
29 2	<<6 10 3 8 2 -12 -8 -21 -16 12]]	Nautilus	2.548	49/48 55/54 245/242
29 10	<<7 2 18 19 -13 9 6 36 37 -9]]		4.023	55/54 225/224 245/242
29 13	<<8 -6 4 1 -28 -16 -26 26 23 -11]]	Wilsec	3.911	49/48 121/120 225/224
29 11	<<9 15 19 12 3 5 -12 2 -24 -32]]	Ammonite	3.980	55/54 100/99 686/675
29 7	<<10 7 5 23 -12 -20 2 -8 29 47]]		4.064	49/48 55/54 625/616
29 9	<<11 -1 20 5 -27 1 -30 49 15 -55]]		5.264	121/120 225/224 1225/1188
29 1	<<17 9 23 13 -25 -11 -38 28 -1 -43]]		5.913	121/120 625/616 686/675
29 8	<<13 12 21 27 -11 -3 -2 15 21 3]]		4.823	55/54 245/242 625/616
29 5	<<14 4 7 9 -26 -28 -34 5 7 1]]		4.725	49/48 121/120 625/616

13-limit temperaments

Period generator	Wedgie	Name	Complexity	Commas
29 12	<<1 -8 -14 -18 -21 -15 -25 -32 -37 -10 -14 -19 -2 -7 -6]]	Cassandra	3.911	100/99 105/104 196/195 245/242
29 6	<<2 13 1 22 16 16 -4 28 18 -34 6 -11 58 41 -26]]	Impunity	3.934	49/48 91/90 100/99 352/351
29 4	<<3 5 16 4 -5 1 17 -4 -19 23 -8 -30 -44 -73 -32]]	Porky	3.380	55/54 65/64 91/90 100/99
29 3	<<4 -3 2 15 3 -14 -8 10 -10 13 45 18 35 1 -45]]	Negroni	2.793	49/48 55/54 65/64 91/90
29 14	<<5 18 17 26 11 17 13 24 -1 -11 -2 -41 14 -32 -58]]		4.312	91/90 100/99 169/168 245/242
29 2	<<6 10 3 8 19 2 -12 -8 8 -21 -16 7 12 42 36]]	Nautilus	2.806	49/48 55/54 91/90 100/99
29 10	<<7 2 -11 -10 -2 -13 -37 -40 -29 -31 -30 -12 10 35 30]]	Roman	4.163	65/64 100/99 105/104 245/242
29 13	<<8 -6 4 1 6 -28 -16 -26 -20 26 23 36 -11 2 17]]	Wilsec	3.527	49/48 65/64 91/90 121/120
29 11	<<9 15 19 12 14 3 5 -12 -11 2 -24 -23 -32 -31 4]]	Ammonite	3.582	55/54 91/90 100/99 169/168
29 7	<<10 7 5 23 22 -12 -20 2 -2 -8 29 25 47 43 -9]]		3.888	49/48 55/54 91/90 847/845
29 9	<<11 -1 -9 5 1 -27 -45 -30 -39 -18 15 6 45 36 -15]]		4.743	65/64 121/120 169/168 275/273
29 1	<<12 20 6 16 9 4 -24 -16 -30 -42 -32 -53 24 3 -28]]		4.724	49/48 55/54 245/242 343/338
29 8	<<13 12 21 27 17 -11 -3 -2 -21 15 21 -5 3 -30 -41]]		4.362	55/54 91/90 169/168 245/242
29 5	<<14 4 7 9 25 -26 -28 -34 -12 5 7 43 1 44 53]]		4.713	49/48 91/90 121/120 625/616